Burst effect of Silicon Photomultiplier (SiPM) at cryogenic temperatures have been discovered few years ago looking at the dark count rate of SiPMs at liquid nitrogen temperatures. Bursts are trains of single signals that happen randomly and are clearly distinguishable from the primary DCR and correlated noise because of their particular time distribution. In this article we describe a detailed study related to both the external causes that triggers bursts and to the phenomenon, internal to the sensor, that produces this dark signals. We related the burst occurrence to the luminescence produced by some trapping centers in the SiPMs when they are excited by ionizing radiation that impinges on the sensor.

We propose a model for the QCD running coupling constant based on the analytical inverse QCD coupling constant concept with an additional regularization in the low momentum region. Analyticity in the $q^2$-complex plane, where q is the four-momentum transfer, is imposed by methods of the Analytic Perturbation Theory. The model incorporates a peculiar low-momentum behavior for ${\alpha }_s(q^2)$ as a divergence at $q^2=0$ to retrieve color confinement, without spoiling its correct high-momentum behavior. This was achieved by means of a two-parameter regularization function, for which we considered three possible analytic expressions. In fact, within the framework of the Analytic Perturbation Theory, ${\alpha }_s(q^2)$ assumes a finite value for $q^2=0$, at all perturbative orders (infrared stability), hence the infrared divergence cannot be implemented. For this reason, we found it more straightforward to work with its reciprocal, namely, ${\epsilon }_s(q^2)=1/{\alpha }_s(q^2)$, imposing its vanishing at the origin of the $q^2$-complex plane via the multiplication of the aforementioned regularizing functions and the spectral density. Once the two free parameters of the regularization functions were settled by fitting to the experimental values of ${\alpha }_s(q^2)$ at the momenta where these data were available and reliable, the model could reproduce the QCD running coupling constant at any other momentum transferred.